Question
If Triangle M N O is congruent to triangle N M O, what statement best describes triangle MON?
The triangle is scalene.
The triangle is equilateral.
The triangle is isosceles and possibly equilateral.
The triangle is isosceles but definitely not equilateral.
The triangle is scalene.
The triangle is equilateral.
The triangle is isosceles and possibly equilateral.
The triangle is isosceles but definitely not equilateral.
Answers
Answered by
GPT-4o mini
Since triangle MNO is congruent to triangle NMO, it means that these two triangles have the same shape and size. However, this congruence does not provide information about the specific lengths of the sides or the measures of the angles.
To determine the type of triangle MON, we note that the letters suggest that the vertices of triangle MNO and triangle NMO are the same, but arranged differently. Therefore the properties of the triangles will depend on the angles and the lengths of the sides, which we can't ascertain from the information given.
However, even without specific measures, we can infer the following based on the definition of congruence:
- Congruence implies that corresponding sides and angles are equal.
- Given that both triangles MNO and NMO share side MN (which is common to both triangles), triangle MON also shares these properties.
Therefore, since the sides of triangle MON can be equal (including shared vertices and sides from congruence), the best characterization, without more specific size information, is that triangle MON is **isoceles but definitely not equilateral** since it has at least two congruent sides if not mentioned otherwise.
Yes, it's correct that the correct statement among your options is:
**The triangle is isosceles but definitely not equilateral.**
To determine the type of triangle MON, we note that the letters suggest that the vertices of triangle MNO and triangle NMO are the same, but arranged differently. Therefore the properties of the triangles will depend on the angles and the lengths of the sides, which we can't ascertain from the information given.
However, even without specific measures, we can infer the following based on the definition of congruence:
- Congruence implies that corresponding sides and angles are equal.
- Given that both triangles MNO and NMO share side MN (which is common to both triangles), triangle MON also shares these properties.
Therefore, since the sides of triangle MON can be equal (including shared vertices and sides from congruence), the best characterization, without more specific size information, is that triangle MON is **isoceles but definitely not equilateral** since it has at least two congruent sides if not mentioned otherwise.
Yes, it's correct that the correct statement among your options is:
**The triangle is isosceles but definitely not equilateral.**